Structure of radical cations of saturated heterocyclic compounds with two heteroatoms as studied by electron paramagnetic resonance, electron-nuclear double resonance, and density functional theory calculations

The radical cations of piperazine, morpholine, thiomorpholine, and thioxane were investigated by electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy in a solid Freon matrix. Optimized geometry and magnetic parameters of the radical cations were calculated using a density functional theory (DFT)/Perdew-Burke-Ernzerhof (PBE) method. Both experimental and theoretical results suggest that all the studied species adopt chair (or distorted chair) conformations. No evidence for the boat conformers with intramolecular sigma-bonding between heteroatoms were obtained. In the cases of morpholine and thioxane, the oxygen atoms are characterized by relatively small spin populations, whereas a major part of spin density is located at N and S atoms, respectively. The thiomorpholine radical cation exhibits nearly equal spin population of N and S atoms. In most cases (except for thioxane), the calculated magnetic parameters agree with the experimental data reasonably well.     

Transient solution of a spin exchange model: Correspondence between cidep and relaxation

A procedure for relating CIDEP and relaxation in a Heisenberg spin exchange (HSE) model is presented which considers all the spin states of a radical pair. The method relies on an exact (transient) solution of the radical pair density matrix under realistic assumptions and is illustrated for the simple ·RH spin case. The results are cast in the form of Bloch-type equations and are suitable for describing time-resolved ESR experiments.     

Open-shell reduced density matrix functional theory

Open-shell reduced density matrix functional theory is established by investigating the domain of the exact functional. For spin states that are the ground state, a particularly simple set is found to be the domain. It cannot be generalized to other spin states. A number of conditions satisfied by the exact density matrix functional is formulated and tested for approximate functionals. The exact functional does not suffer from fractional spin error, which is the source of the static correlation error in dissociated molecules. We prove that a simple approximation (called the Buijse-Baerends functional, Mu?ller or square root functional) has a non-positive fractional spin error. In the case of the H atom the error is zero. Numerical results for a few atoms are given for approximate density and density matrix functionals as well as a recently developed range-separated combination of both.     

Magnetic properties of the Fe spin crossover complex in emulsion polymerization of trifluoroethylmethacrylate using poly(vinyl alcohol)

Influence of chemical substitution in the Fe^II spin crossover complex on magnetic properties in emulsion polymerization of trifluoroethylmethacrylate using poly(vinyl alcohol) as a protective colloid was investigated near its high spin/low spin (HS/LS) phase transition. The obvious bi-stability of the HS/LS phase transition was considered by the identification of multiple spin states between the quintet (S=2) states to single state (S=0) across the excited triplet state (S=1). Magnetic parameters of gradual shifts of anisotropy g-tensor supported by the molecular distortion of the spin crossover complex would arise from a Jahn-Teller effect regarding ligand field theory on the basis of a B3LYP density functional theory using electron spin resonance (ESR) spectrum and X-ray powder diffraction.     

Fast computer calculation of ESR and nonlinear spin response spectra from the fast motion to the rigid lattice limits

Fast computer simulation of the electron spin resonance and adiabatic rapid passage spectra of spin labels characterized by rotational correlation times ranging from the fast motion to the rigid lattice limits is demonstrated. Calculations are based upon a modification of the stochastic Liouville equation for the density matrix which explicitly includes interaction of the spins with applied radiation and modulation fields. Several mathematical simplifications of previous calculations are demonstrated, permitting computation with core and CPU requirements compatible with small computers.     

Experimental and Theoretical Study of the n‐Doped Successive Polyanions of Oligocruciform Molecular Wires: Up to Five Units of Charge

The electronic structure of polyanions of sterically encumbered triisopropylsilyl‐substituted linear and cyclic oligo(phenyleneethynylene)s ( M onomer, T rimer, P entamer, and Tr iangle) is investigated by electron paramagnetic resonance (EPR), electron nuclear double resonance (ENDOR), and UV/Vis–near‐infrared (NIR) spectroscopies, cyclic voltammetry, and theoretical calculations (DFT). Increasing anion orders are generated sequentially in vacuo at room temperature by chemical reaction with potassium metal up to the pentaanion. The relevance of these compounds acting as electron reservoirs is thus demonstrated. Even‐order anions are EPR silent, whereas the odd species exhibit different signatures, which are identified after comparison of the measured hyperfine couplings by ENDOR spectroscopy with those predicted by DFT calculations. With increasing size of the oligomers the electron spin density is first distributed over the backbone carbon atoms for the monoanions, and then further localized at the outer phenyl rings for the trianion species. Examination of the UV/Vis‐NIR spectra indicates that the monoanions ( T^.? , P^.? ) exhibit two transitions in the Vis‐NIR region, whereas a strong absorption in the IR region is solely observed for higher reduced states. Electronic transitions of the neutral monoanions and trianions are redshifted with increasing oligomer size, whereas for a given oligomer a blueshift is observed upon increasing the charge, which suggests a localization of the spin density.     

Molecular and electronic structures and magnetic properties of multilayer graphene nanoclusters and their changes under the influence of adsorbed molecules

The results of investigations of the structures and properties of multilayer graphene nano-clusters (nanographites), structural blocks of activated carbon fibers, and their changes under the influence of adsorbed molecules are presented. The presence of specific edge p-electron-ic states in the nanographites and a reversible decrease in their density at the Fermi level upon the interaction of the graphite nanoparticles with adsorbed molecules of oxygen, chlorine, and water were found. The explanation of the discovered effect was proposed in the terms of the model of spin splitting of edge p-electronic states initiated by the transfer of a small fraction of the electron density from the nanographites to adsorbed molecules. The change in the sign of the temperature coefficient of current carrier spin relaxation rate in the presence of adsorbates can be accounted for by their interaction with edge spin-split (magnetically ordered) states. The preservation of peripheral p-electronic states of the nanographites of free (dangling) s-orbitals of edge carbon atoms at saturation with chlorine was substantiated.     

Spin polarized metastable helium de-excitation processes on metal surfaces

Spin polarized de-excitation of a metastable helium atom interacting with metal surfaces is treated within density functional theory. The method is based on a self-consistent calculation of the spin dependent electronic properties of the system, such as the surface density of states and the localized surface states, to compute the transition rate. On the high work function Ag(100) and Ag(111) surfaces, the helium 2s electron is delocalized in the metal and hence the transition rate is weakly spin dependent. The existence of a Shockley surface state in Ag(111) determines a neutralization rate that is about 59% larger than that from Ag(100). On a low work function metal, namely Na(100), the rate is of smaller magnitude than those on silver because the 2s triplet resonance is found to be more occupied. Consequently, emitted electrons can display a strong spin dependence also for a paramagnetic surface.     

The spin distribution in low-spin iron porphyrins

In many low-spin (S = 1/2) iron porphyrin derivatives, electron spin resonance (ESR) spectra indicate that one of the d(pi) orbitals of iron, either a d(xz) or d(yz), depending on the axial ligands of the porphyrin complex as well as their orientation, is essentially singly occupied; the unpaired electron is almost completely located at the metal. In contrast, nuclear magnetic resonance (NMR) and electron nuclear double resonance (ENDOR) spectroscopy convincingly show that a significant share of the unpaired electron is delocalized. This apparent contradiction is explained by the present density-functional-theory (DFT) calculations performed on a heme a model as well as on bis-imidazole-ligated iron porphyrin without substituents. The calculations show that the integrated spin density at the iron atom is nearly one, in agreement with the ESR measurements. However, significant areas with opposite (beta) spin are found along the Fe-N bond axes, thus evoking a need for additional alpha-spin density to be present in the porphyrin ring, ring substituents, and the axial ligands to keep the net amount of unpaired spin exactly one. The gross spin density, that is, the sum of unpaired alpha and beta spins, amounts to about 1.3 electrons. It seems that the degree to which alpha and beta spin dominate in different regions of the heme structure, as evidenced in these calculations, has not been previously observed.     

Matrix formulation of the generalized Hartree-Fock methods

Spin-projected one-particle density and spin density matrices are presented as polynomials of suitable unprojected quantities with generalized Sasaki-Ohno coefficients. Thus an explicit form of Harriman's theorems is given. For the two-particle spatial density matrix an expansion in direct products of powers of unprojected residual electron and spin density matrices is given. For these basic matrices of the scheme the variational spin-extended equations are formulated.     

Some developments in the spin-extended Hartree-Fock method

All the second-order density matrix spin components for the spin-extended Hartree-Fock method are obtained. The coefficients in the final formulae are only ω_sM, ω_sM±1, ω_sM±2, where ω_sM are the weights of pure states of spin s in the initial unprojected determinant with spin projection M. The eigenvalue problem for the best electron density natural orbitals in the spin-extended method is formulated. All the second-order transition density matrix spin components between pure spin basis functions built of orthogonal orbitals and distinguished by different core choice are also found. This basis may be used on CI calculations.     

Effect of N-methylation of macrocyclic amine ligands on the spin state of iron(III): a tale of two fluoro complexes

Syntheses and characterization of [(cyclamacetate)FeF]PF6 (1) and the corresponding N-methylated complex [(trimethylcyclamacetate)FeF]PF6 (3) are presented. Compound 1 is prepared in good yields from the analogous chloro complex, whereas 3 is prepared by hydrolysis of the oxo-bridged diiron compound (Me3cyclam-acetate)Fe-O-FeCl3 (2) in the presence of PF(6) anions. Magnetic susceptibility and spectroscopic data including electron paramagnetic resonance and M?ssbauer spectra indicate that 1 contains low-spin Fe(III) (S = 1/2), while 3 is high spin (S = 5/2). Both octahedral fluoro complexes were investigated theoretically by density functional theory in order to determine why the spin states of the two molecules are different. Energies calculated using the B3LYP functional correctly predict 1 to have a low-spin S = 1/2 ground state and 3 to be high spin, regardless of whether a solvation model is included. The difference between 1 and 3 is most likely a combination of steric effects caused by the N-methyl groups, which compel the Fe-N bond distances to be longer in 3 than they ordinarily would be, and also electronic effects, which cause the N-methylated ligand to be a weaker sigma donor than its nonmethylated counterpart.     

Energy spectrum of extended Hubbard model with spin‐dependent hopping and related spin ladder model

We studied the energy spectrum of the 1‐D extended Hubbard model with spin‐dependent hopping and related spin ladder system formed by two coupled XXZ spin 1/2 chains with the interchain interaction of Ising type. It was proved that the model excitation spectrum has no gap excepting some special values of z‐projection of the ground‐state total spin. The thorough analytic consideration of two‐magnon states was given. The existence up to five bound states at specified value of quasimomentum of the pair of inverted spins was shown. We also present the results of density matrix renormalization group calculations that showed nonadequacy of the pair approximation for n‐magnon bound states of the extended model with the strong electron–electron interactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Density matrix in the open shell theory

All the second-order density matrix spin components for the spin-projected Slater determinant are presented as expansions in direct products of powers of unprojected spin- and residual electron density matrices. Spin components of the second-order transition density matrices between spin-projected Slater determinants built of orthogonal orbitals are also obtained.     

Electronic dimensions of FeMo-co, the active site of nitrogenase, and its catalytic intermediates

The iron-molybdenum cofactor (FeMo-co), which is the catalytic center for the enzymatic conversion of N(2) to NH(3), has the composition [NFe(7)MoS(9)(homocitrate)], and, with a cluster of eight transition metal atoms and nine sulfur atoms, has a complex delocalized electronic structure. The electronic dimensions of FeMo-co and of each of its derivatives appear as sets of electronic states lying close in energy. These electronic dimensions naturally partner the geometrical changes and the reactivity patterns during the catalytic cycle, and also connect with spectroscopic investigations of the mechanism. This paper describes straightforward computational procedures for the determination and management of the low-lying electronic states of FeMo-co and of its coordinated intermediates and transition states during density functional simulations of steps in the catalytic mechanism. General principles for the distribution of electron spin density over all atoms are presented, using several proposed intermediates as examples. A tough general irony arises in the distribution of spin density over FeMo-co and its derivatives: the less interesting atoms get the spin, and the most interesting atoms do not.     

On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix

In this paper we propose a functional of the many-body cumulant of the second-order reduced density matrix within the spin-free formalism of quantum chemistry which quantifies the idea of electron correlation and allows one to detect spin entanglement. Its properties are rigorously stated and discussed for spin-adapted pure states. Numerical determinations are performed for both equilibrium conformations and dissociation processes in molecular systems.     

High resolution electron paramagnetic resonance spectroscopy of quintet pyridyl-2,6-dinitrene in solid argon: magnetic properties and molecular structure

The high resolution X-band electron para magnetic resonance (EPR) spectrum of quintet pyridyl-2,6-dinitrene was recorded after the photolysis of 4-amino-2,6-diazido-3,5-dichloropyridine in solid argon matrix at 15 K. This spectrum represents a new type of powder EPR spectra that are characteristic for quintet spin states with zero-field splitting parameters |E(q)/D(q)| approximately 1/4. All EPR lines of the quintet dinitrene were unambiguously assigned based on the eigenfield calculations of the Zeeman energy levels and angular dependencies of resonance magnetic fields. Owing to the high resolution of the experimental EPR spectrum, zero-field splitting parameters of the quintet dinitrene were determined with a high accuracy: D(q)=0.2100+/-0.0005 cm(-1) and E(q)=-0.0560+/-0.0002 cm(-1). These parameters provide correct information regarding the molecular angle Theta and distance r between two triplet sites in the molecule of quintet dinitrene. The measured molecular angle Theta=114.2 degrees+/-0.2 degrees is in excellent agreement with results of the density functional theory calculations. The analysis of the magnetic parameters shows that the spin population on the nitrene units in the quintet dinitrene is greater than that on the nitrene unit in the triplet nitrene.